Bulletin des Sciences Mathematiques最新文献

{"title":"On character variety of Anosov representations","authors":"Krishnendu Gongopadhyay,&nbsp;Tathagata Nayak","doi":"10.1016/j.bulsci.2025.103621","DOIUrl":"10.1016/j.bulsci.2025.103621","url":null,"abstract":"<div><div>Let Γ be the fundamental group of a <em>k</em>-punctured, <span><math><mi>k</mi><mo>≥</mo><mn>0</mn></math></span>, closed connected orientable surface of genus <span><math><mi>g</mi><mo>≥</mo><mn>2</mn></math></span>. We show that the character variety of the <span><math><mo>(</mo><msup><mrow><mi>Q</mi></mrow><mrow><mo>+</mo></mrow></msup><mo>,</mo><msup><mrow><mi>Q</mi></mrow><mrow><mo>−</mo></mrow></msup><mo>)</mo></math></span>-Anosov irreducible representations, resp. the character variety of the <span><math><mo>(</mo><msup><mrow><mi>P</mi></mrow><mrow><mo>+</mo></mrow></msup><mo>,</mo><msup><mrow><mi>P</mi></mrow><mrow><mo>−</mo></mrow></msup><mo>)</mo></math></span>-Anosov Zariski dense representations of Γ into <span><math><mrow><mi>SL</mi></mrow><mo>(</mo><mi>n</mi><mo>,</mo><mi>C</mi><mo>)</mo></math></span>, <span><math><mi>n</mi><mo>≥</mo><mn>2</mn></math></span>, is a complex manifold of complex dimension <span><math><mo>(</mo><mn>2</mn><mi>g</mi><mo>+</mo><mi>k</mi><mo>−</mo><mn>2</mn><mo>)</mo><mo>(</mo><msup><mrow><mi>n</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>−</mo><mn>1</mn><mo>)</mo></math></span>. For <span><math><mi>Γ</mi><mo>=</mo><msub><mrow><mi>π</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>(</mo><msub><mrow><mi>Σ</mi></mrow><mrow><mi>g</mi></mrow></msub><mo>)</mo></math></span>, we also show that these character varieties are holomorphic symplectic manifolds.</div></div>","PeriodicalId":55313,"journal":{"name":"Bulletin des Sciences Mathematiques","volume":"202 ","pages":"Article 103621"},"PeriodicalIF":1.3,"publicationDate":"2025-03-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143760968","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A q-congruence implying the Beukers–Van Hamme congruence","authors":"Victor J.W. Guo ,&nbsp;Ji-Cai Liu","doi":"10.1016/j.bulsci.2025.103615","DOIUrl":"10.1016/j.bulsci.2025.103615","url":null,"abstract":"&lt;div&gt;&lt;div&gt;By making use of Andrews' terminating &lt;em&gt;q&lt;/em&gt;-analogue of Watson's formula and a double sum identity, we give a &lt;em&gt;q&lt;/em&gt;-analogue of the following congruence: for any prime &lt;span&gt;&lt;math&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;mo&gt;≡&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mrow&gt;&lt;mi&gt;mod&lt;/mi&gt;&lt;/mrow&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;mn&gt;4&lt;/mn&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt;,&lt;span&gt;&lt;span&gt;&lt;span&gt;&lt;math&gt;&lt;munderover&gt;&lt;mo&gt;∑&lt;/mo&gt;&lt;mrow&gt;&lt;mi&gt;k&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;/&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/munderover&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mtable&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;/&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;mi&gt;k&lt;/mi&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;/mtable&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mtable&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;/&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mi&gt;k&lt;/mi&gt;&lt;/mrow&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;mi&gt;k&lt;/mi&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;/mtable&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;mo&gt;≡&lt;/mo&gt;&lt;mfrac&gt;&lt;mrow&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;/&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;/mrow&gt;&lt;/mfrac&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mtable&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;/&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;/&lt;/mo&gt;&lt;mn&gt;4&lt;/mn&gt;&lt;/mrow&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;/mtable&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mrow&gt;&lt;mi&gt;mod&lt;/mi&gt;&lt;/mrow&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;.&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt; In view of the Chowla–Dwork–Evans congruence, our &lt;em&gt;q&lt;/em&gt;-congruence may somewhat be regarded as a &lt;em&gt;q&lt;/em&gt;-analogue of the Beukers–Van Hamme congruence:&lt;span&gt;&lt;span&gt;&lt;span&gt;&lt;math&gt;&lt;munderover&gt;&lt;mo&gt;∑&lt;/mo&gt;&lt;mrow&gt;&lt;mi&gt;k&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;/&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/munderover&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mtable&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;/&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;mi&gt;k&lt;/mi&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;/mtable&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mtable&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;/&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mi&gt;k&lt;/mi&gt;&lt;/mrow&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;mi&gt;k&lt;/mi&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;/mtable&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;mo&gt;≡&lt;/mo&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;/&lt;/mo&gt;&lt;mn&gt;4&lt;/mn&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;mi&gt;a&lt;/mi&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mfrac&gt;&lt;mrow&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;mi&gt;a&lt;/mi&gt;&lt;/mrow&gt;&lt;/mfrac&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mrow&gt;&lt;mi&gt;mod&lt;/mi&gt;&lt;/mrow&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt; where &lt;span&gt;&lt;math&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;a&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;b&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;/math&gt;&lt;/span&gt; with &lt;span&gt;&lt;math&gt;&lt;mi&gt;a&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;b&lt;/mi&gt;&lt;","PeriodicalId":55313,"journal":{"name":"Bulletin des Sciences Mathematiques","volume":"201 ","pages":"Article 103615"},"PeriodicalIF":1.3,"publicationDate":"2025-03-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143682036","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On global well-posedness, scattering and other properties for infinity energy solutions to the inhomogeneous NLS equation","authors":"Roger P. de Moura,&nbsp;Mykael Cardoso,&nbsp;Gleison N. Santos","doi":"10.1016/j.bulsci.2025.103620","DOIUrl":"10.1016/j.bulsci.2025.103620","url":null,"abstract":"<div><div>In this work, we consider the inhomogeneous nonlinear Schrödinger (INLS) equation in <span><math><msup><mrow><mi>R</mi></mrow><mrow><mi>n</mi></mrow></msup></math></span><span><span><span><math><mrow><mi>i</mi><msub><mrow><mo>∂</mo></mrow><mrow><mi>t</mi></mrow></msub><mi>u</mi><mo>+</mo><mi>Δ</mi><mi>u</mi><mo>+</mo><mi>γ</mi><mo>|</mo><mi>x</mi><msup><mrow><mo>|</mo></mrow><mrow><mo>−</mo><mi>b</mi></mrow></msup><mo>|</mo><mi>u</mi><msup><mrow><mo>|</mo></mrow><mrow><mi>α</mi></mrow></msup><mi>u</mi><mo>=</mo><mn>0</mn><mo>,</mo></mrow></math></span></span></span> where <span><math><mi>γ</mi><mo>=</mo><mo>±</mo><mn>1</mn></math></span>, and <em>α</em> and <em>b</em> are positive numbers. Our main focus is to establish the global well-posedness of the INLS equation in Lorentz spaces for <span><math><mn>0</mn><mo>&lt;</mo><mi>b</mi><mo>&lt;</mo><mn>2</mn></math></span> and <span><math><mi>α</mi><mo>&lt;</mo><mfrac><mrow><mn>4</mn><mo>−</mo><mn>2</mn><mi>b</mi></mrow><mrow><mi>N</mi><mo>−</mo><mn>2</mn></mrow></mfrac></math></span>. To achieve this, we use Strichartz estimates in Lorentz spaces <span><math><msup><mrow><mi>L</mi></mrow><mrow><mi>r</mi><mo>,</mo><mi>q</mi></mrow></msup><mo>(</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>n</mi></mrow></msup><mo>)</mo></math></span> combined with a fixed point argument. Working on Lorentz space setting instead the classical <span><math><msup><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msup></math></span> is motivated by the fact that the potential <span><math><mo>|</mo><mi>x</mi><msup><mrow><mo>|</mo></mrow><mrow><mo>−</mo><mi>b</mi></mrow></msup></math></span> does not belong the usual <span><math><msup><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msup></math></span>-space. As a consequence of the ideas developed here on the global solution study we obtain some other properties for INLS, such as, existence of self-similar solutions, scattering, wave operators and asymptotic stability.</div></div>","PeriodicalId":55313,"journal":{"name":"Bulletin des Sciences Mathematiques","volume":"201 ","pages":"Article 103620"},"PeriodicalIF":1.3,"publicationDate":"2025-03-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143697012","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Some new Lucas sequence versions of Wolstenholme's congruence","authors":"Yanteng Lu ,&nbsp;Peng Yang ,&nbsp;Tianxin Cai","doi":"10.1016/j.bulsci.2025.103619","DOIUrl":"10.1016/j.bulsci.2025.103619","url":null,"abstract":"<div><div>In this paper, we extend the results of He, Mao, and Togbé, as well as Yang and Yang, and give some Lucas sequence versions generalizations of Wolstenholme's theorem with multiple harmonic sums.</div></div>","PeriodicalId":55313,"journal":{"name":"Bulletin des Sciences Mathematiques","volume":"202 ","pages":"Article 103619"},"PeriodicalIF":1.3,"publicationDate":"2025-03-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143686003","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Sparse bounds for maximal oscillatory rough singular integral operators","authors":"Surjeet Singh Choudhary ,&nbsp;Saurabh Shrivastava ,&nbsp;Kalachand Shuin","doi":"10.1016/j.bulsci.2025.103612","DOIUrl":"10.1016/j.bulsci.2025.103612","url":null,"abstract":"&lt;div&gt;&lt;div&gt;In this paper, we prove sparse bounds for the maximal oscillatory rough singular integral operator&lt;span&gt;&lt;span&gt;&lt;span&gt;&lt;math&gt;&lt;msubsup&gt;&lt;mrow&gt;&lt;mi&gt;T&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;Ω&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mo&gt;⁎&lt;/mo&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;P&lt;/mi&gt;&lt;/mrow&gt;&lt;/msubsup&gt;&lt;mi&gt;f&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;:&lt;/mo&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;munder&gt;&lt;mi&gt;sup&lt;/mi&gt;&lt;mrow&gt;&lt;mi&gt;ϵ&lt;/mi&gt;&lt;mo&gt;&gt;&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/mrow&gt;&lt;/munder&gt;&lt;mo&gt;⁡&lt;/mo&gt;&lt;mrow&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;munder&gt;&lt;mo&gt;∫&lt;/mo&gt;&lt;mrow&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mi&gt;y&lt;/mi&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;mo&gt;&gt;&lt;/mo&gt;&lt;mi&gt;ϵ&lt;/mi&gt;&lt;/mrow&gt;&lt;/munder&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;e&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;ι&lt;/mi&gt;&lt;mi&gt;P&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;y&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mfrac&gt;&lt;mrow&gt;&lt;mi&gt;Ω&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mi&gt;y&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;/&lt;/mo&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mi&gt;y&lt;/mi&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mi&gt;y&lt;/mi&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;/mrow&gt;&lt;/mfrac&gt;&lt;mi&gt;f&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;y&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mi&gt;d&lt;/mi&gt;&lt;mi&gt;y&lt;/mi&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;/mrow&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt; where &lt;span&gt;&lt;math&gt;&lt;mi&gt;P&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;y&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt; is a real-valued polynomial on &lt;span&gt;&lt;math&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;R&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo&gt;×&lt;/mo&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;R&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;/math&gt;&lt;/span&gt; and &lt;span&gt;&lt;math&gt;&lt;mi&gt;Ω&lt;/mi&gt;&lt;mo&gt;∈&lt;/mo&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;L&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;∞&lt;/mo&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;S&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt; is a homogeneous function of degree zero with &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mo&gt;∫&lt;/mo&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;S&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mi&gt;Ω&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;θ&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;mi&gt;d&lt;/mi&gt;&lt;mi&gt;θ&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/math&gt;&lt;/span&gt;. This allows us to conclude weighted &lt;span&gt;&lt;math&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;L&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;/math&gt;&lt;/span&gt;-estimates for the operator &lt;span&gt;&lt;math&gt;&lt;msubsup&gt;&lt;mrow&gt;&lt;mi&gt;T&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;Ω&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mo&gt;⁎&lt;/mo&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;P&lt;/mi&gt;&lt;/mrow&gt;&lt;/msubsup&gt;&lt;/math&gt;&lt;/span&gt;. Moreover, the norm &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mo&gt;‖&lt;/mo&gt;&lt;msubsup&gt;&lt;mrow&gt;&lt;mi&gt;T&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;Ω&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mo&gt;⁎&lt;/mo&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;P&lt;/mi&gt;&lt;/mrow&gt;&lt;/msubsup&gt;&lt;mo&gt;‖&lt;/mo&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;L&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;ω&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;→&lt;/mo&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;L&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;ω&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt; depends only on the total degree of the polynomial &lt;span&gt;&lt;math&gt;&lt;mi&gt;P&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;y&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt;, but not on the coefficients of &lt;span&gt;&lt;math&gt;&lt;mi&gt;P&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;y&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt;. Finally, we will show that these techniques also apply to obtain sparse bounds for oscillatory rough singular integral operator &lt;span&gt;&lt;math&gt;&lt;msubsup&gt;&lt;mrow&gt;&lt;mi&gt;T&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;Ω&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;P&lt;/mi&gt;&lt;/mrow&gt;&lt;/msubsup&gt;&lt;/math&gt;&lt;/spa","PeriodicalId":55313,"journal":{"name":"Bulletin des Sciences Mathematiques","volume":"201 ","pages":"Article 103612"},"PeriodicalIF":1.3,"publicationDate":"2025-03-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143682037","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Seshadri constants and related conjectures over characteristic zero fields","authors":"Ashima Bansal,&nbsp;Souradeep Majumder","doi":"10.1016/j.bulsci.2025.103617","DOIUrl":"10.1016/j.bulsci.2025.103617","url":null,"abstract":"<div><div>In this article, we study Seshadri constants over a base field <em>k</em>, which is of characteristic zero and not necessarily algebraically closed. We provide an upper bound for them and also discuss their behaviour under base change. Additionally, we examine Segre's Conjecture, Harbourne-Hirschowitz's Conjecture, and Nagata's Conjecture, discussing their interrelations in this setting.</div></div>","PeriodicalId":55313,"journal":{"name":"Bulletin des Sciences Mathematiques","volume":"202 ","pages":"Article 103617"},"PeriodicalIF":1.3,"publicationDate":"2025-03-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143686071","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Maximal functions of the multilinear pseudo-differentials operators","authors":"Liang Huang","doi":"10.1016/j.bulsci.2025.103618","DOIUrl":"10.1016/j.bulsci.2025.103618","url":null,"abstract":"<div><div>In this paper, we consider the maximal multilinear pseudo-differential operator with symbols <span><math><mi>σ</mi><mo>∈</mo><mi>B</mi><msubsup><mrow><mi>S</mi></mrow><mrow><mn>1</mn><mo>,</mo><mi>δ</mi></mrow><mrow><mn>0</mn></mrow></msubsup><mo>(</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>n</mi></mrow></msup><mo>×</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>m</mi><mi>n</mi></mrow></msup><mo>)</mo></math></span>, and establish the <span><math><msup><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msup></math></span> estimate with a sharp bound <span><math><mi>O</mi><mo>(</mo><msqrt><mrow><mi>log</mi><mo>⁡</mo><mo>(</mo><mi>N</mi><mo>+</mo><mn>2</mn><mo>)</mo></mrow></msqrt><mo>)</mo></math></span>. Our work improves the work of Chen, Dai and Lu <span><span>[5]</span></span> by extending the symbol <em>σ</em> from the Hörmander class <span><math><mi>B</mi><msubsup><mrow><mi>S</mi></mrow><mrow><mn>1</mn><mo>,</mo><mn>0</mn></mrow><mrow><mn>0</mn></mrow></msubsup></math></span> to <span><math><mi>B</mi><msubsup><mrow><mi>S</mi></mrow><mrow><mn>1</mn><mo>,</mo><mi>δ</mi></mrow><mrow><mn>0</mn></mrow></msubsup></math></span> with <span><math><mn>0</mn><mo>≤</mo><mi>δ</mi><mo>&lt;</mo><mn>1</mn></math></span>. The main tools such as localizing the maximal pseudo-differential operators and the time-frequency analysis in <span><span>[5]</span></span> may not accommodate symbols <span><math><mi>σ</mi><mo>∈</mo><mi>B</mi><msubsup><mrow><mi>S</mi></mrow><mrow><mn>1</mn><mo>,</mo><mi>δ</mi></mrow><mrow><mn>0</mn></mrow></msubsup><mo>(</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>n</mi></mrow></msup><mo>×</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>m</mi><mi>n</mi></mrow></msup><mo>)</mo></math></span> with <span><math><mn>0</mn><mo>&lt;</mo><mi>δ</mi><mo>&lt;</mo><mn>1</mn></math></span>. In this work, we handle this difficulty by applying the inhomogeneous Littlewood-Paley-Stein decomposition to the space variable and using Taylor's expansion to track the size of those decomposed pieces. Then together with the ideas of using martingales, some related pointwise estimates and the good-<em>λ</em> inequality as in <span><span>[16]</span></span>, <span><span>[19]</span></span>, we will be able to obtain the boundedness with the optimal bound.</div></div>","PeriodicalId":55313,"journal":{"name":"Bulletin des Sciences Mathematiques","volume":"202 ","pages":"Article 103618"},"PeriodicalIF":1.3,"publicationDate":"2025-03-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143686004","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Decomposable abelian G-curves and special subvarieties","authors":"Irene Spelta ,&nbsp;Carolina Tamborini","doi":"10.1016/j.bulsci.2025.103616","DOIUrl":"10.1016/j.bulsci.2025.103616","url":null,"abstract":"<div><div>We consider families of abelian Galois coverings of the line. When the Jacobian of the general element is totally decomposable, i.e., is isogenous to a product of elliptic curves, we prove that they yield special subvarieties of <span><math><msub><mrow><mi>A</mi></mrow><mrow><mi>g</mi></mrow></msub></math></span> if and only if a numerical condition holds, which in the general case is only known to be sufficient.</div></div>","PeriodicalId":55313,"journal":{"name":"Bulletin des Sciences Mathematiques","volume":"201 ","pages":"Article 103616"},"PeriodicalIF":1.3,"publicationDate":"2025-03-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143682035","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Compactness criterions for certain commutators of oscillatory singular integrals","authors":"Chenyan Wang ,&nbsp;Huoxiong Wu ,&nbsp;Weijin Yan","doi":"10.1016/j.bulsci.2025.103613","DOIUrl":"10.1016/j.bulsci.2025.103613","url":null,"abstract":"<div><div>Let Ω be homogeneous of degree zero, integrable and have mean zero on <span><math><msup><mrow><mi>S</mi></mrow><mrow><mi>n</mi><mo>−</mo><mn>1</mn></mrow></msup></math></span>, <span><math><mi>P</mi><mo>(</mo><mi>x</mi><mo>,</mo><mi>y</mi><mo>)</mo></math></span> be a real-valued polynomial on <span><math><msup><mrow><mi>R</mi></mrow><mrow><mi>n</mi></mrow></msup><mo>×</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>n</mi></mrow></msup></math></span>. Define the oscillatory singular integral <span><math><msubsup><mrow><mi>T</mi></mrow><mrow><mi>Ω</mi></mrow><mrow><mi>P</mi></mrow></msubsup></math></span> by<span><span><span><math><msubsup><mrow><mi>T</mi></mrow><mrow><mi>Ω</mi></mrow><mrow><mi>P</mi></mrow></msubsup><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>=</mo><mrow><mi>p</mi><mo>.</mo><mi>v</mi><mo>.</mo></mrow><munder><mo>∫</mo><mrow><msup><mrow><mi>R</mi></mrow><mrow><mi>n</mi></mrow></msup></mrow></munder><msup><mrow><mi>e</mi></mrow><mrow><mi>i</mi><mi>P</mi><mo>(</mo><mi>x</mi><mo>,</mo><mi>y</mi><mo>)</mo></mrow></msup><mfrac><mrow><mi>Ω</mi><mo>(</mo><mi>x</mi><mo>−</mo><mi>y</mi><mo>)</mo></mrow><mrow><mo>|</mo><mi>x</mi><mo>−</mo><mi>y</mi><msup><mrow><mo>|</mo></mrow><mrow><mi>n</mi></mrow></msup></mrow></mfrac><mi>f</mi><mo>(</mo><mi>y</mi><mo>)</mo><mi>d</mi><mi>y</mi><mo>.</mo></math></span></span></span> This paper is devoted to studying the compactness of <span><math><mo>[</mo><mi>b</mi><mo>,</mo><msubsup><mrow><mi>T</mi></mrow><mrow><mi>Ω</mi></mrow><mrow><mi>P</mi></mrow></msubsup><mo>]</mo></math></span>, the commutators formed by <span><math><msubsup><mrow><mi>T</mi></mrow><mrow><mi>Ω</mi></mrow><mrow><mi>P</mi></mrow></msubsup></math></span> with <span><math><mi>b</mi><mo>∈</mo><msubsup><mrow><mi>L</mi></mrow><mrow><mtext>loc</mtext></mrow><mrow><mn>1</mn></mrow></msubsup><mo>(</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>n</mi></mrow></msup><mo>)</mo></math></span>. Several compactness criteria of <span><math><mo>[</mo><mi>b</mi><mo>,</mo><msubsup><mrow><mi>T</mi></mrow><mrow><mi>Ω</mi></mrow><mrow><mi>P</mi></mrow></msubsup><mo>]</mo></math></span> on Lebesgue spaces and Morrey spaces are given. As applications, the compactness of <span><math><mo>[</mo><mi>b</mi><mo>,</mo><msubsup><mrow><mi>T</mi></mrow><mrow><mi>Ω</mi></mrow><mrow><mi>P</mi></mrow></msubsup><mo>]</mo></math></span> with rough kernels on Lebesgue spaces and Morrey spaces is obtained.</div></div>","PeriodicalId":55313,"journal":{"name":"Bulletin des Sciences Mathematiques","volume":"201 ","pages":"Article 103613"},"PeriodicalIF":1.3,"publicationDate":"2025-03-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143682034","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On near orthogonality of the Banach frames for the wave packet spaces","authors":"Dimitri Bytchenkoff","doi":"10.1016/j.bulsci.2025.103611","DOIUrl":"10.1016/j.bulsci.2025.103611","url":null,"abstract":"&lt;div&gt;&lt;div&gt;In solving scientific, engineering or pure mathematical problems one is frequently faced with a need to approximate the function of a given class with a specified precision by the linear combination of a preferably small number of simpler functions. This can often achieved by choosing the simpler functions localised one way or another both in the time and frequency domain. Constructing a set of linearly independent functions, let alone a basis, with a given time-frequency localisation is a formidable and often unsolvable problem, though. A much better chance one stands in building a set of time-frequency localised functions that constitutes a so-called frame – a generalisation of the notion of the basis, whose elements need not be linear independent, rather than a basis.&lt;/div&gt;&lt;div&gt;Over the last seventy years or so, a range of frames have been designed to allow the decomposition and synthesis of functions of various classes. The most prominent examples of such systems are Gabor functions, wavelets, ridgelets, curvelets, shearlets and wave atoms. We recently introduced a family of quasi-Banach spaces – which we called &lt;span&gt;&lt;math&gt;&lt;mi&gt;w&lt;/mi&gt;&lt;mi&gt;a&lt;/mi&gt;&lt;mi&gt;v&lt;/mi&gt;&lt;mi&gt;e&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt; &lt;span&gt;&lt;math&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;mi&gt;a&lt;/mi&gt;&lt;mi&gt;c&lt;/mi&gt;&lt;mi&gt;k&lt;/mi&gt;&lt;mi&gt;e&lt;/mi&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt; &lt;span&gt;&lt;math&gt;&lt;mi&gt;s&lt;/mi&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;mi&gt;a&lt;/mi&gt;&lt;mi&gt;c&lt;/mi&gt;&lt;mi&gt;e&lt;/mi&gt;&lt;mi&gt;s&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt; – that encompasses all those classes of functions whose elements have sparse expansions in one of the above-mentioned frames, supplied them with Banach frames – the kind of frames that ensure that any element of the class of functions for which a frame was designed can be decomposed and reconstructed using that frame – and provided their atomic decomposition. Herein we prove that the Banach frames for and sets of atoms of the wave packet spaces – which we call &lt;span&gt;&lt;math&gt;&lt;mi&gt;w&lt;/mi&gt;&lt;mi&gt;a&lt;/mi&gt;&lt;mi&gt;v&lt;/mi&gt;&lt;mi&gt;e&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt; &lt;span&gt;&lt;math&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;mi&gt;a&lt;/mi&gt;&lt;mi&gt;c&lt;/mi&gt;&lt;mi&gt;k&lt;/mi&gt;&lt;mi&gt;e&lt;/mi&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt; &lt;span&gt;&lt;math&gt;&lt;mi&gt;s&lt;/mi&gt;&lt;mi&gt;y&lt;/mi&gt;&lt;mi&gt;s&lt;/mi&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;mi&gt;e&lt;/mi&gt;&lt;mi&gt;m&lt;/mi&gt;&lt;mi&gt;s&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt; – are indeed localised in the time and frequency domain or, more specifically, that they are near orthogonal; and therefore so are all of the above-mentioned examples of frames.&lt;/div&gt;&lt;div&gt;We shall also show that, unlike those examples, the wave packet system can be made to assume a wide range of types and degrees of time-frequency localisation by the suitable choice of values of the parameters of the system. This, we believe, makes the wave packet systems not only suitable for decomposing, synthesising or approximating functions of a wide range of quasi-Banach function spaces in an efficient and effective way, but also for their use for representing linear bounded operators on the quasi-Banach spaces by sparse and well structured matrices using the Galerkin method. This, in its turn, should allow one to design efficient computer programs for solving corresponding operator equations on t","PeriodicalId":55313,"journal":{"name":"Bulletin des Sciences Mathematiques","volume":"201 ","pages":"Article 103611"},"PeriodicalIF":1.3,"publicationDate":"2025-03-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143643317","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}